Coarsening and thermalization properties of a quenched ferromagnetic spin-1 condensate

Abstract

We examine the dynamics of a quasi-two-dimensional spin-1 condensate in which the quadratic Zeeman energy q is suddenly quenched to a value where the system has a ferromagnetic ground state. There are two distinct types of ferromagnetic phases, i.e. a range of q values where the magnetization prefers to be in the direction of the external field (easy-axis), and a range of q values where it prefers to be transverse to the field (easy-plane). We study the quench dynamics for a variety of q values and show that there is a single dynamic critical exponent to characterize the scale invariant domain growth for each ferromagnetic phase. For both quenches we give simple analytic models that capture the essential scale invariant dynamics, and correctly predict the exponents. Because the order parameter for each phase is different, the natures of the domains and the relevant topological defects in each type of coarsening is also different. To explore these differences we characterize the fractal dimension of the domain walls, and the relationship of polar-core spin vortices to the domains in the easy-plane phase. Finally, we consider how the energy liberated from the quench thermalizes in the easy-axis quench. We show that local equilibrium is established in the spin waves on moderate time scales, but continues to evolve as the domains anneal.

Violation of single-length-scaling dynamics via spin vortices in an isolated spin-1 Bose gas

“…Universal scaling with exponent β 1/2 has recently been observed experimentally in a ferromagnetic spin-1 Bose gas in a near-1D geometry [10]. Theoretical studies have shown that universal scaling can occur in the ordering process of one-and quasi twodimensional (quasi-2D) spin-1 as well as binary Bose gases after a parameter quench into an ordered phase [11][12][13][14][15][16][17][18][19].…”

Experimentally Accessible Invariants Encoded in Interparticle Correlations of Harmonically Trapped Ultra-cold Few-Fermion Mixtures

“…The two-body problem [11] is an example but the separation can also be done for larger number of particles [12][13][14]26,27] at the cost of using more sophisticated methods of describing the relative motion [15,22]. In practice, the mentioned transformation of variables is difficult to perform straightforwardly, however it is a standard tool in a theoretical analysis of few-body problems [30][31][32]. In the following we will separate the the centre-of-mass motion within the scope of the second quantisation formalizm.…”

Domain percolation in a quenched ferromagnetic spinor condensate

“…Simulations are performed using the spin-1 GPE with weak noise (representing the vacuum fluctuations) added to seed the dynamic instabilities. The noise is added to the polar condensate state as described in [39] and then the spin rotations described in the previous subsection are applied to this state to prepare the initial condition. The simulation is performed on a 2D square grid of spatial dimension L×L covered by a grid of N N L Ĺ equally spaced points, with periodic boundary conditions.…”

“…( ) [21,39]. In this regime the system should exhibit the phenomenon of 'phase-ordering percolation' [27], whereby the effective size of the system diminishes in time as L l t d ( ).…”